Active Approaches to Vibration Absorption through Antiresonance Assignment: A Comparative Study

Abstract

Vibration absorption is a core research topic in structural dynamics and the mechanics of machines, and antiresonance assignment is an effective solution to such a problem in the presence of harmonic excitation forces. Due to recent developments in the theory of feedback control systems, the use of active control approaches to antiresonance assignment has been recently gaining more attention in the literature. Therefore, several methods exploiting state feedback or output feedback have been proposed in recent years. These techniques that just rely on servo-controlled actuators are becoming an interesting alternative to active approaches that emulate the well-known Tuned Mass Damper in an active (or semi-active) framework. This paper reviews and compares the most important approaches, with a greater focus on the methods exploiting the concept of control theory without adding new degrees of freedom in the system. The theoretical results, with the underlying theory, are discussed to highlight the key features of each assignment techniques. Several numerical examples where different techniques are applied and compared, also providing some analysis usually neglected in the literature, enrich the paper and demonstrate the key concepts.

Robust Assignment of Natural Frequencies and Antiresonances in Vibrating Systems through Dynamic Structural Modification

“…and the receptance matrix H(ω) � (−ω 2 M + K) −1 is introduced, such that q(ω) � H(ω)f(ω). e r, c entry of H(ω), denoted by h rc (ω), is the transfer function from the external force applied at the c-th coordinate to the displacement of the r-th coordinate, which can be computed through Cramer's rule of linear system as follows [22,23,40]:…”

“…For example, ensuring insensitive natural (or resonance) frequencies is of great importance in the design of resonators (such as feeders [26,37] or sonotrodes [20,38]), where the resonance frequency should match the excitation frequency regardless of the changes in some parameters, to ensure large motion with small actuation effort. In the case of vibration absorption of harmonic excited systems, assigning antiresonances at the excitation frequency is an effective approach ( [39][40][41]), that should be ensured even in the case of changes of some system parameters. Generally speaking, any application where passive EA is performed can benefit of this approach, since increasing robustness allows to get rid of small parameter changes, compared to the nominal model, of uncertainty in the nominal parameters.…”

Robotics and Vibration Mechanics

“…Compliant mechanism design methods encompass finite element analysis, topology optimization, and pseudo-rigid-body model methods [8]. Design methods can include, for instance, the modal modification of a predefined mechanical system [9], the assignment of proper eigenfrequencies [10], as well as vibration absorption techniques [11]. A further approach that exploits the elastic behavior of a mechanism is the natural motion [12,13], which allows for energy saving in cyclic tasks by properly designing compliant elements [14], and by considering the free vibration response of the system [15].…”

Modeling, Design and Optimization of Flexible Mechanical Systems

“…Richiedei and Tamellin [56] Active approaches to vibration absorption through antiresonance assignment: A comparative study reviews and contrasts methods for the assignment of resonance frequencies and mode shapes.…”